Matrix dimensions in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What function in R is used to find the dimensions of a matrix?

The dim() function returns the number of rows and columns of a matrix as a vector.

beginner

How do you create a 3x2 matrix in R?

Use matrix(data, nrow = 3, ncol = 2). For example, matrix(1:6, nrow = 3, ncol = 2) creates a matrix with 3 rows and 2 columns filled with numbers 1 to 6.

intermediate

What does dim() return if applied to a vector in R?

It returns NULL because vectors do not have dimensions like matrices do.

intermediate

How can you change the dimensions of a vector to make it a matrix?

Assign a dimension attribute using dim(vector) <- c(rows, columns). For example, dim(v) <- c(2,3) turns vector v into a 2x3 matrix.

beginner

What is the difference between nrow() and ncol() functions in R?

nrow() returns the number of rows of a matrix, while ncol() returns the number of columns.

What does dim(matrix(1:6, nrow=2, ncol=3)) return?

A [1] 2 3

B [1] 3 2

C [1] 6

D NULL

dim() returns the number of rows and columns. Here, 2 rows and 3 columns.

If v <- 1:6, what does dim(v) return?

A 6

B NULL

C [1] 1 6

D [1] 6 1

Vectors do not have dimensions, so dim() returns NULL.

How do you convert a vector v of length 6 into a 2x3 matrix?

A Use <code>dim(v) <- c(2,3)</code>

B Use <code>matrix(v, nrow=3, ncol=2)</code>

C Use <code>length(v) <- c(2,3)</code>

D Use <code>dim(v) <- c(3,2)</code>

Assigning dim(v) <- c(2,3) changes the vector into a 2-row, 3-column matrix.

What does ncol(matrix(1:4, nrow=2)) return?

A 3

B 4

C NULL

D 2

ncol() returns the number of columns. Here, the matrix has 2 columns.

Which function gives the number of rows in a matrix?

A length()

B ncol()

C nrow()

D dim()

nrow() returns the number of rows in a matrix.

Explain how to find and change the dimensions of a matrix in R.

Think about how you check size and how you can turn a vector into a matrix.

Describe the difference between a vector and a matrix in terms of dimensions in R.

Consider what dim() returns for each.

Practice

1. What does the dim() function return when used on a matrix in R?

easy

A. The first element of the matrix

B. The sum of all elements in the matrix

C. A vector with the number of rows and columns

D. The matrix converted to a vector

Solution

1. Step 1: Understand the purpose of dim()

   The dim() function in R returns the dimensions of an object, typically a matrix or array.

2. Step 2: What does it return for a matrix?

   For a matrix, dim() returns a vector of length two: the number of rows and the number of columns.

3. Final Answer:

   A vector with the number of rows and columns -> Option C

4. Quick Check:

   dim(matrix) = c(rows, columns) [OK]

Hint: Remember dim() gives rows and columns together [OK]

Common Mistakes:

• Thinking dim() returns sum of elements
• Confusing dim() with length()
• Expecting dim() to return matrix elements

2. Which of the following is the correct way to create a 3x2 matrix in R?

easy

A. matrix(1:6, nrow=3, ncol=2)

B. matrix(1:6, nrow=2, ncol=3)

C. matrix(1:6, rows=3, cols=2)

D. matrix(1:6, 3, 2, byrow=TRUE)

Solution

1. Step 1: Check the matrix function parameters

   The matrix() function uses nrow and ncol to specify rows and columns.

2. Step 2: Identify correct parameter names and values

   matrix(1:6, nrow=3, ncol=2) uses nrow=3 and ncol=2, which correctly creates a 3-row, 2-column matrix.

3. Final Answer:

   matrix(1:6, nrow=3, ncol=2) -> Option A

4. Quick Check:

   Use nrow and ncol to set dimensions [OK]

Hint: Use nrow and ncol to set matrix size [OK]

Common Mistakes:

• Using wrong parameter names like rows or cols
• Swapping nrow and ncol values
• Omitting parameter names causing confusion

3. What is the output of the following R code?

m <- matrix(1:12, nrow=3, ncol=4)
dim(m)

medium

A. [1] 12

B. [1] 4 3

C. [1] 3

D. [1] 3 4

Solution

1. Step 1: Understand matrix creation

   The matrix m is created with 3 rows and 4 columns using nrow=3 and ncol=4.

2. Step 2: Check the output of dim(m)

   The dim() function returns a vector with the number of rows and columns, so it returns 3 4.

3. Final Answer:

   [1] 3 4 -> Option D

4. Quick Check:

   dim(m) = c(3, 4) [OK]

Hint: dim() returns rows then columns vector [OK]

Common Mistakes:

• Confusing order of rows and columns
• Expecting dim() to return total elements
• Misreading output as a single number

4. Identify the error in this R code snippet:

m <- matrix(1:9, nrow=3, ncol=3)
dim(m) <- c(2, 5)

medium

A. The code is correct and runs without error

B. You cannot assign dimensions that don't match the number of elements

C. dim() cannot be used on matrices

D. The matrix function is missing the byrow argument

Solution

1. Step 1: Check the original matrix size

   The matrix m has 9 elements (3 rows x 3 columns).

2. Step 2: Analyze the dimension assignment

   Assigning dim(m) <- c(2, 5) tries to reshape m to 2 rows and 5 columns, which requires 10 elements, not 9.

3. Final Answer:

   You cannot assign dimensions that don't match the number of elements -> Option B

4. Quick Check:

   New dims must match total elements [OK]

Hint: New dimensions must multiply to total elements [OK]

Common Mistakes:

• Ignoring element count mismatch
• Thinking dim() cannot be assigned
• Assuming byrow affects dimension assignment

5. You have a matrix m with dimensions 4x5. You want to reshape it into a matrix with 5 rows. Which of the following commands correctly changes the dimensions without losing data?

hard

A. dim(m) <- c(5, 4)

B. dim(m) <- c(5, 5)

C. dim(m) <- c(5, 3)

D. dim(m) <- c(5, 2)

Solution

1. Step 1: Calculate total elements in original matrix

   The original matrix has 4 rows x 5 columns = 20 elements.

2. Step 2: Check which new dimension matches total elements

   dim(m) <- c(5, 4) sets dimensions to 5 rows and 4 columns, which is 20 elements, matching original size.

3. Step 3: Verify other options

   Options B, C, and D have total elements 25, 15, and 10 respectively, which do not match 20, causing errors or data loss.

4. Final Answer:

   dim(m) <- c(5, 4) -> Option A

5. Quick Check:

   New dims must multiply to 20 [OK]

Hint: New rows x new cols = total elements [OK]

Common Mistakes:

• Choosing dimensions that don't match total elements
• Swapping rows and columns incorrectly
• Forgetting to check total element count